Remove the Klima and turn on the AC at the PBU. Check for +12V at pin 10. If that checks, jump pins 7 and 10 to send power directly to the compressor. If that doesn't work, check the compressor clutch gap and the wiring to the compressor.

AFAIK the pressure switch at the dryer is upstream of the Klima. Doesn't hurt to jump the brown connectors to make sure the pressure switch isn't the problem.

The tach and Klima take an engine rpm signal from the flywheel sensor below the oil filter. It's a parallel feed - AC will work with no tach and tach will work with no Klima.

EDIT - Get a second opinion on this because my memory is sketchy. It could be that the PBU sends a ground signal to the Klima to engage the compressor. If so then mup pins 5 and 10 to engage the compressor.

Sixto